| Study of the Wada fractal boundary and indeterminate crisis |
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| 作者姓名： | 洪灵 徐健学 |
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| 作者单位： | Institute of Nonlinear Dynamics, Xi'an Jiaotong University, Xi'an 710049, China;Institute of Nonlinear Dynamics, Xi'an Jiaotong University, Xi'an 710049, China |
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| 基金项目： | Project supported by the National Natural Science Foundation of China (Grant Nos 10172067 and 19972051). |
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| 摘 要： | By using the generalized cell mapping digraph (GCMD)method,we study bifurcations governing the escape of periodically forced oscillators in a potential well,in which a chaotic saddle plays an extremely important role.Int this paper,we find the chaotic saddle,and we demonstrate that the chaotic saddle is embedded in a strange fractal boundary which has the Wada property,that any point on the boundary of that basin is also simultaneously on the boundary of at least two other basins.The chaotic saddle in the Wada fractal boundary,by colliding with a chaotic attractor,leads to a chaotic boundary crisis with a global indeterminate outcome which presents an extreme form of indeterminacy in a dynamical system.We also investigate the origin and evolution of the chaotic saddle in the Wada fractal boundary particularly concentrating on its discontinuous bifurcations(metamorphoses),We demonstrate that the chaotic saddle in the Wada fractal boundary is created by the collision between two chaotic saddles in different fractal boundaries.After a final escape bifurcation,there only exists the attractor at infinity;a chaotic saddle with a beautiful pattern is left behind in phase space.
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| 关 键 词： | 浑沌 Wada分维边界 不确定性危害 |
| 收稿时间： | 2001-12-30 |
Study of the Wada fractal boundary and indeterminate crisis |
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| Hong Ling and Xu Jian-Xue.Study of the Wada fractal boundary and indeterminate crisis[J].Chinese Physics B,2002,11(11):1115-1123. |
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| Authors: | Hong Ling and Xu Jian-Xue |
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| Affiliation: | Institute of Nonlinear Dynamics, Xi'an Jiaotong University, Xi'an 710049, China |
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| Abstract: | By using the generalized cell mapping digraph (GCMD) method, we study bifurcations governing the escape of periodically forced oscillators in a potential well, in which a chaotic saddle plays an extremely important role. In this paper, we find the chaotic saddle, and we demonstrate that the chaotic saddle is embedded in a strange fractal boundary which has the Wada property, that any point on the boundary of that basin is also simultaneously on the boundary of at least two other basins. The chaotic saddle in the Wada fractal boundary, by colliding with a chaotic attractor, leads to a chaotic boundary crisis with a global indeterminate outcome which presents an extreme form of indeterminacy in a dynamical system. We also investigate the origin and evolution of the chaotic saddle in the Wada fractal boundary, particularly concentrating on its discontinuous bifurcations (metamorphoses). We demonstrate that the chaotic saddle in the Wada fractal boundary is created by the collision between two chaotic saddles in different fractal boundaries. After a final escape bifurcation, there only exists the attractor at infinity; a chaotic saddle with a beautiful pattern is left behind in phase space. |
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| Keywords: | global analysis generalized cell mapping indeterminate chaotic boundary crisis chaotic saddle Wada fractal boundary |
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